48$0<HT`l x     ,8DP\ht!"#$ % & ' ( )*+,-./01234/  H        d 0 # gi( f$%&'(( LB)'*-14>@@(@Yield @ APR + points (lender's view) 8.00 APR + 2 pointsYears 'til loan paid off (refinanced)Yield (APY)Yield @ Year vM'POINTS1.WK1 - Yield on a loan w/points - 4Apr96 rev 30Apr01,1Oct02/JRA >'A loan with points understates the yield to the lender.6'A loan with points front-loads the yield curve.('========== INPUTS: =============='Initial loan amount j@8!'Normalizing linear numbers to a log-normal number'Interest, APR  @!'Transformed # =5#'constant*(@ln(data)-@ln(dataMin))/@ln(dataMax) 'Points @ 'Term, months  v@! 'Linear Distrib 1-30 #  $  %  & '  ( ( '===== Computer calculates =======! 'Normalized 0-1 =%# %# % ( % %$ +?%# % ( % %% <'?%# % ( % %& (?%# % ( % %' !vYi/?%# % ( % %( ?%# % ( %  'PMT (Mo.)( _@d  8 'Yield on APR b4 Pts/ Dz" @ dd      'Net loan after Points& @ d   ! " # $ % & ' ( ) * + , - . / 0 1''Create log-time (3 lines below):('Null value, Y low-limit labels ->                                    ! " $ % & ' ( * + , - . / 0 1 2 3 4('Labels, X, log-tranformed time ->                                    $ % & ' ( * + , - . / 0 1 2 3 4('Log-transformed time ----------->%%% % %+?%% % %<'?%% % %+?%% % %V-H?%% % %T?%% % %\%N?%% % % :`w?%% % % <'?%% % % (?%% % % L{?%% % % :8a?%% % %!?%% % %ţVV?%% % %5ςz?%% % %+?%% % %Apo?%% % %ߤ1?%% % %:M޳?%% % %!vYi/?%% % %-?%% % %͸?%% % %X{ ?%% % %i?%% % %V-H?%% % % g U?%% % %M[;?%% % %.oY?%% % %X?%% % %?%% % !!%% % !"%% %  #!$+?%% % !%+?%% %  &!'<'?%% % !(<'?%% %  )!*(?%% % !+(?%% %  ,!-!vYi/?%% % !.!vYi/?%% %  /!0?%% % !1?%% %  2 3 4'Years to refinancing =  ? @ @ @ @ @ @  @ "@ $@ &@ (@ *@ ,@ .@ 0@ 1@ 2@ 3@ 4@ 5@ 6@ 7@ 8@ 9@ :@ ;@ <@ =@ >@$'YIELD = 100*((1+irr)^12-1) = 'x04%@d    'RU"@d    'K)C"@d    'Vm!@d    '=!@d    'xwwˊ!@d    '/Rq!@d    ' x^!@d    ' JlO!@d    ' C!@d    ' BB+:!@d    ' N3!@d    '=&-!@d    '_a(!@d    '2O#!@d    'r# !@d    '*a !@d    'ɛ!@d    '?}U!@d    'xeM~!@d    'DR!@d    '!@d    'z]5!@d    '8!@d    '.y!@d    'ex!@d    '#%!@d    'H}!@d    'DϢ!@d    '`!@d    'IRR (pPR, monthly) =#p!E?{Gz?ڀY#D1?{Gz?ڀY#KI}?{Gz?ڀY#w]}?{Gz?ڀY#Ԓz}?{Gz?ڀY#KE0Wi|?{Gz?ڀY#$|?{Gz?ڀY# |?{Gz?ڀY# `n|?{Gz?ڀY# ]g<#n\|?{Gz?ڀY# 0M|?{Gz?Y# QvB|?{Gz?ڀY#pyU8|?{Gz?ڀY# ;0|?{Gz?ڀY#9r)|?{Gz?ڀY##|?{Gz?ڀY#)$|?{Gz?ڀY#⤫|?{Gz?ڀY#МOb|?{Gz?jY#oabx|?{Gz?jY#9!|?{Gz?jY#@6_@ 6_@ 6_@ 6_@ 6_@  6_@  6_@  6_@  6_@  6_@ 6_@ 6_@ 6_@ 6_@ 6_@ 6_@ 6_@ 6_@ 6_@ 6_@ 6_@ 6_@ 6_@ 6_@ 6_@ 6_@ 6_@ 6_@  7?@7_@ 7_@ 7_@ 7_@ 7_@  7_@  7_@  7_@  7_@  7_@ 7_@ 7_@ 7_@ 7_@ 7_@ 7_@ 7_@ 7_@ 7_@ 7_@ 7_@ 7_@ 7_@ 7_@ 7_@ 7_@ 7_@ 7_@  8@@8_@ 8_@ 8_@ 8_@ 8_@  8_@  8_@  8_@  8_@  8_@ 8_@ 8_@ 8_@ 8_@ 8_@ 8_@ 8_@ 8_@ 8_@ 8_@ 8_@ 8_@ 8_@ 8_@ 8_@ 8_@ 8_@ 8_@  9@@9_@ 9_@ 9_@ 9_@ 9_@  9_@  9_@  9_@  9_@  9_@ 9_@ 9_@ 9_@ 9_@ 9_@ 9_@ 9_@ 9_@ 9_@ 9_@ 9_@ 9_@ 9_@ 9_@ 9_@ 9_@ 9_@ 9_@  :A@:_@ :_@ :_@ :_@ :_@  :_@  :_@  :_@  :_@  :_@ :_@ :_@ :_@ :_@ :_@ :_@ :_@ :_@ :_@ :_@ :_@ :_@ :_@ :_@ :_@ :_@ :_@ :_@  ;A@;_@ ;_@ ;_@ ;_@ ;_@  ;_@  ;_@  ;_@  ;_@  ;_@ ;_@ ;_@ ;_@ ;_@ ;_@ ;_@ ;_@ ;_@ ;_@ ;_@ ;_@ ;_@ ;_@ 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